Entanglement-assisted detection of fading targets via correlation-to-coherence conversion

Quantum illumination utilizes an entanglement-enhanced sensing system to outperform classical illumination in detecting a suspected target, despite the entanglement-breaking loss and noise. However, practical and optimal receiver design to fulfil the quantum advantage has been a long open problem. Recently, [arXiv:2207.06609] proposed the correlation-to-displacement (`C$\rightarrow$D') conversion module to enable an optimal receiver design that greatly reduces the complexity of the previous known optimal receiver [Phys. Rev. Lett. {\bf 118}, 040801 (2017)]. There, the analyses of the conversion module assume an ideal target with a known reflectivity and a fixed return phase. In practical applications, however, targets often induce a random return phase; moreover, their reflectivities can have fluctuations obeying a Rayleigh-distribution. In this work, we extend the analyses of the C$\rightarrow$D module to realistic targets and show that the entanglement advantage is maintained albeit reduced. In particular, the conversion module allows exact and efficient performance evaluation despite the non-Gaussian nature of the quantum channel involved.